 # Section 5: The Strong Force: QCD, Hadrons, and the Lightness of Pions

The other force, in addition to the electromagnetic force, that plays a significant role in the structure of the atom is the strong nuclear force. Like the electromagnetic force, the strong force can create bound states that contain several particles. Their bound states, such as nuclei, are around 10-15 meters in diameter, much smaller than atoms, which are around 10-10 meters across. It is the energy stored in the bound nuclei that is released in nuclear fission, the reaction that takes place in nuclear power plants and nuclear weapons, and nuclear fusion, which occurs in the center of our Sun and of other stars.

## Confined quarks

We can define charge as the property particles can have that allow them to interact via a particular force. The electromagnetic force, for example, occurs between particles that carry electric charge. The value of a particle's electric charge determines the details of how it will interact with other electrically charged particles. For example, electrons have one unit of negative electric charge. They feel electromagnetic forces when they are near positively charged protons, but not when they are near electrically neutral neutrinos, which have an electric charge of zero. Opposite charges attract, so the electromagnetic forces tends to create electrically neutral objects: Protons and electrons come together and make atoms, where the positive and negative charges cancel. Neutral atoms can still combine into molecules, and larger objects, as the charged parts of the atoms attract each other. Figure 15: Neutralized charges in QED and QCD.

At the fundamental particle level, it is quarks that feel the strong force. This is because quarks have the kind of charge that allows the strong force to act on them. For the strong force, there are three types of positive charge and three types of negative charge. The three types of charge are labeled as colors—a quark can come in red, green, or blue. Antiquarks have negative charge, labeled as anti-red, etc. Quarks of three different colors will attract each other and form a color-neutral unit, as will a quark of a given color and an antiquark of the same anti-color. As with the atom and the electromagnetic force, baryons such as protons and neutrons are color-neutral (red+green+blue=white), as are mesons made of quarks and antiquarks, such as pions. Protons and neutrons can still bind and form atomic nuclei, again, in analogy to the electromagnetic force binding atoms into molecules. Electrons and other leptons do not carry color charge and therefore do not feel the strong force.

In analogy to quantum electrodynamics, the theory of the strong force is called quantum chromodynamics, or QCD. The force carrier of the strong force is the gluon, analogous to the photon of electromagnetism. A crucial difference, however, is that while the photon itself does not carry electromagnetic charge, the gluon does carry color charge—when a quark emits a gluon, that actually changes its color. Because of this, the strong force binds particles together much more tightly. Unlike the electromagnetic force, whose strength decreases as the inverse square distance between two charged particles (that is, as 1/r2, where r is the distance between particles), the strong force between a quark and antiquark remains constant as the distance between them grows.

Figure 16: As two bound quarks are pulled apart, new quarks pop out of the vacuum.

The gluon field is confined to a tube that extends from the quark to the antiquark because, in a sense, the exchanged gluons themselves are attracted to each other. These gluon tubes have often been called strings. In fact, the birth of string theory came from an attempt to describe the strong interactions. It has moved on to bigger and better things, becoming the leading candidate for the theory of quantum gravity as we'll see in Unit 4.

As we pull bound quarks apart, the gluon tube cannot grow indefinitely. That is because it contains energy. Once the energy in the tube is greater than the energy required to create a new quark and antiquark, the pair pops out of the vacuum and cuts the tube into two smaller, less energetic, pieces. This fact—that quarks pop out of the vacuum to form new hadrons—has dramatic implications for collider experiments, and explains why we do not find single quarks in nature.

## Particle jets

Particle collisions involving QCD can look very different than those involving QED. When a proton and an antiproton collide, one can imagine it as two globs of jelly hurling toward each other. Each glob has a few marbles embedded in them. When they collide, once in a while two marbles find each other, make a hard collision, and go flying out in some random direction with a trail of jelly following. The marbles represent quarks and gluons, and in the collision, they are being torn from the jelly that is the proton. Figure 17: In this Feynman diagram of a jet, a single quark decays into a shower of quarks and gluons.

However, we know quarks cannot be free, and that if quarks are produced or separated in a high-energy collision, the color force starts ripping quark/anti-quark pairs out of the vacuum. The result is a directed spray, or jet of particles headed off in the direction the individual quark would have gone. This can be partially described by a Feynman diagram where, for example, a quark becomes a shower of quarks and gluons.

In the early days of QCD, it became clear that if a gluon is produced with high energy after a collision, it, too, would form a jet. At that point, experimentalists began to look for physical evidence of gluons. In 1979, a team at the newly built PETRA electron-positron storage ring at DESY, Germany's Deutsches Elektronen-Synchrotron, found the evidence, in the form of several of the tell-tale three-jet events. Other groups quickly confirmed the result, and thus established the reality of the gluon.

## A confining force

As we have seen, the strength of the strong force changes depending on the energy of the interaction, or the distance between particles. At high energies, or short distances, the strong force actually gets weaker. This was discovered by physicists David Gross, David Politzer, and Frank Wilczek, who received the 2004 Nobel Prize for this work. In fact, the color charge (or coupling) gets so weak at high energies, you can describe the interactions between quarks in colliding protons as the scattering of free quarks; marbles in jelly are a good metaphor. Figure 18: The QCD coupling depends on energy.

At lower energies, or longer distances, the charge strength appears to hit infinity, or blows up as physicists like to say. As a result, protons may as well be a fundamental particle in low-energy proton-proton collisions because the collision energy isn’t high enough to probe their internal structure. In this case, we say that the quarks are confined. This qualitative result is clear in experiments, however, "infinity" doesn't make for good quantitative predictions. This difficulty keeps QCD a lively and active area of research.

Physicists have not been able to use QCD theory to make accurate calculations of the masses and interactions of the hadrons made of quarks. Theorists have developed a number of techniques to overcome this issue, the most robust being lattice gauge theory. This takes a theory like QCD, and puts it on a lattice, or grid of points, making space and time discrete rather than continuous. And because the number of points is finite, the situation can be simulated on a computer. Amazingly enough, physicists studying phenomena at length scales much longer than the defined lattice point spacing find that the simulated physics acts as if it is in continuous space. So, in theory, all one needs to do to calculate the mass of a hadron is to space the lattice points close enough together. The problem is that the computing power required for a calculation grows exponentially with the number of points on the lattice. One of the main hurdles to overcome in lattice gauge theory at this point is the computer power needed for accurate calculations.

## The pion puzzle

The energy scale where the QCD coupling blows up is in fact the mass of most hadrons—roughly 1 GeV. There are a few exceptions, however. Notably, pions are only about a seventh the mass of the proton. These particles turn out to be a result of spontaneous symmetry breaking in QCD as predicted by the so-called Nambu-Goldstone theorem that we will learn more about in Section 8.

Japanese physicist Hideki Yukawa predicted the existence of the pion, a light spinless particle, in 1935. Yukawa actually thought of the pion as a force carrier of the strong force, long before QCD and the weak forces were understood, and even before the full development of QED. Yukawa believed that the pion mediated the force that held protons and neutrons together in the nucleus. We now know that pion exchange is an important part of the description of low-energy scattering of protons and neutrons.

Yukawa's prediction came from using the Heisenberg uncertainty principle in a manner similar to what we did in Section 2 when we wanted to understand the exchange of force carriers. Heisenberg's uncertainty principle suggests that a virtual particle of a certain energy (or mass) tends to exist for an amount of time (and therefore tends to travel a certain distance) that is proportional to the inverse of its energy. Yukawa took the estimated distance between protons and neutrons in the nucleus and converted it into an energy, or a mass scale, and predicted the existence of a boson of that mass. This idea of a heavy exchange particle causing the force to only work at short distances becomes the central feature in the next section.